diff options
| -rw-r--r-- | mdpoly/algebra.py | 25 |
1 files changed, 22 insertions, 3 deletions
diff --git a/mdpoly/algebra.py b/mdpoly/algebra.py index 4342a5e..480a904 100644 --- a/mdpoly/algebra.py +++ b/mdpoly/algebra.py @@ -139,7 +139,7 @@ def unary_operator(inner_type: AlgebraicStructure): *right* contains a placeholder :py:class:`mdpoly.leaves.Nothing`, furthermore a new field *inner* is added as alias to *left*. - See also :py:fun:`mdpoly.algebra.binary_operator`. + See also :py:func:`mdpoly.algebra.binary_operator`. """ def decorator(cls: Expr) -> Expr: """ Class decorator to modify constructor of unary operators. """ @@ -239,7 +239,11 @@ class Exp(Expr, ReducibleExpr): # ╹ ┗━┛┗━╸ ╹ ╹ ╹┗━┛╹ ╹╹╹ ╹┗━╸ ╹ ╹┗━╸┗━┛┗━╸┗━┛╹┗╸╹ ╹ class PolyRingAlgebra(AlgebraicStructure, Protocol): - """ Endows with the algebraic structure of a polynomial ring. """ + r""" Endows with the algebraic structure of a polynomial ring. + + This is the algebra of :math:`\mathbb{R}[x_1, \ldots, x_n]`. Note that the + polynomials are scalars. + """ _algebra = AlgebraicStructure.Algebra.poly_ring _parameter = Param _constant = Const @@ -367,7 +371,22 @@ class RationalFieldAlgebra(AlgebraicStructure, Protocol): # ╹ ╹╹ ╹ ╹ ╹┗╸╹╹ ╹ ╹ ╹┗━╸┗━┛┗━╸┗━┛╹┗╸╹ ╹ class MatrixAlgebra(AlgebraicStructure, Protocol): - """ Endows with the algebraic structure of a matrix ring. """ + r""" Endows with the algebraic structure of a matrix ring and / or module + depending on the shape. + + We denote with :math:`R` a polynomial ring. + + - If the shape is square, like :math:`(n, n)` then this is :math:`M_n(R)` + the ring of matrices over :math:`R`. + + - If the shape is something else like a row or column (:math:`(m, p)`, + :math:`(1, n)` or :math:`(n, 1)`) this is a module, i.e. an algebra with + addition and scalar multiplication, where the "scalars" come from + :math:`R`. + + Furthermore some operators that are usually expected from matrices are + already included (eg. transposition). + """ _algebra = AlgebraicStructure.Algebra.matrix_ring # FIXME: consider MatParam or something like that? |